On the energy decay rates for the 1D damped fractional Klein–Gordon equation

Local decay for the damped wave equation in the energy space

Exponential Decay Rates for the Damped Korteweg-de Vries Type Equation

The exponential decay rate of L−norm related to the Korteweg-de Vries equation with localized damping posed on the whole real line is established. In addition, using classical arguments we determine that the solutions associated to the fully damped Korteweg-de Vries equation do not decay in H− level for arbitrary initial data.

Optimal Blowup Rates for the Minimal Energy Null Control for the Structurally Damped Abstract Wave Equation

The null controllability problem for a structurally damped abstract wave equation–a socalled elastic model–is considered with a view towards obtain optimal rates of blowup for the associated minimal energy function Emin(T ), as terminal time T ↓ 0. Key use is made of the underlying analyticity of the elastic generator A, as well as of the explicit characterization of its domain of definition. W...

Energy decay for the damped wave equation under a pressure condition

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by...

Energy Decay of Damped Systems

We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the generated semigroup is shown to be bounded by the upper real part of the numerical range of the underlying quadratic operator pencil.